Signal Processing - Research Paper Example

One of these digital signal processing techniques is adaptive filtering. Adaptive Filters Haykin (2006) defines an adaptive filter as a system which is self-designing and reliant on a recursive algorithm for its operation. This feature enables an adaptive to satisfactorily perform in an environment where there is scarce or no knowledge of the applicable statistics. Diniz & Netto (2002) observe that an adaptive filter is used when either the fixed specifications are not known, or these specifications cannot be met by filters which are time-invariant.

Adaptive filter’s characteristics depend on the input signal and such filters are time-varying because their parameters continually change so as to satisfy a performance requirement. The two main groups of adaptive filters are linear and nonlinear. According to Stearns & Widrow (1985), linear adaptive filters calculate an approximation of the desired response by utilizing a linear permutation of the available group of observables that are applied to the filter’s input. Nonlinear adaptive filters are those that depend on the input signal and their parameters change continually.

Also, adaptive filters can be classified as supervised and unsupervised adaptive filters. Supervised adaptive filters apply the presence of a training series that gives different outputs of a desired ouput for a particular input signal. The response that is desired is compared against the real output due to the input signal, and the error signal that results is used in adjusting the filter’s free parameters. Unsupervised adaptive filters perform alterations of their free parameters without the requirement for a desired response.

Such filters are designed with a group of rules that enable it to calculate the input-output mapping with particular desirable properties (Sayed, 2003). Adaptive Filtering System Configuration Drumright (1998) establishes 4 major types of adaptive filtering configurations. These include adaptive noise cancellation, adaptive inverse system, adaptive system identification and adaptive linear prediction. Algorithm implementation in all these systems, but the configuration is different. They all have the same general characteristics which include: an input signal x(n), a desired result d(n), an output signal y(n), an adaptive transfer function w(n) and an error signal e(n). e(n)=d(n)-y(n) The adaptive system identification determines a discrete approximation of the transfer function for an unknown analog or digital system.

A similar input x(n) is applied to both the unknown system and the adaptive filter and the outputs are compared. The y(n) of the adaptive filter is subtracted from that of the unknown resulting in an error signal e(n) which is used to manipulate the filter coefficients of the adaptive system. In the adaptive noise cancellation configuration, an input x(n) and a noise source N1(n) are compared with a desired signal d(n) which comprises of a signal s(n) corrupted by another noise N0(n). The adaptive filter coefficients adapt to cause the error signal to be a noiseless version of the signal s(n).

The adaptive linear prediction configuration performs two operations; linear prediction and noise cancellation. Finally, the adaptive inverse system models the inverse of the unknown system u(n), an aspect which is useful in adaptive equalization (Drumright, 1998). Conclusion Just as discussed above, the classical applications of adaptive filt